By G. David Forney Jr. (auth.), Marc Fossorier, Hideki Imai, Shu Lin, Alain Poli (eds.)
This booklet constitutes the refereed complaints of the nineteenth overseas Symposium on utilized Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-13, held in Honolulu, Hawaii, united states in November 1999.
The forty two revised complete papers offered including six invited survey papers have been rigorously reviewed and chosen from a complete of 86 submissions. The papers are geared up in sections on codes and iterative deciphering, mathematics, graphs and matrices, block codes, earrings and fields, interpreting equipment, code development, algebraic curves, cryptography, codes and interpreting, convolutional codes, designs, interpreting of block codes, modulation and codes, Gröbner bases and AG codes, and polynomials.
Read or Download Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 13th International Symposium, AAECC-13 Honolulu, Hawaii, USA, November 15–19, 1999 Proceedings PDF
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Additional info for Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 13th International Symposium, AAECC-13 Honolulu, Hawaii, USA, November 15–19, 1999 Proceedings
Theorem 3 (Cliﬀord’s Theorem). Let N be a normal subgroup in G of prime index p, and let F be an irreducible representation of CN . For a ﬁxed g ∈ G \ N , let T denote the transversal (1, g, g 2 , . . , g p−1 ) of the cosets of N in G. Then exactly one of the following two cases applies. i (1) All F g are equivalent. Then there are exactly p irreducible representations D0 , . . , Dp−1 of CG extending F . The Dk are pairwise inequivalent and satisfy F ↑G ∼ D0 ⊕ . . ⊕ Dp−1 . Moreover, if χ0 , χ1 , .
Then, by Cliﬀord’s Theorem, there are exactly p := pi pairwise nonequivalent irreducible extensions D0 , . . , Dp−1 of F to CGi satisfying Dk =χk ⊗ D0 , where χ0 , χ1 , . . , χp−1 are the irreducible characters of the cyclic group Gi /Gi−1 . Since Dk ↓ Gi−1 = F , k = 1, . . , p − 1, in this step only the Dk (gi ) have to be computed. One can show that Dk (gi ) ∈ Int(F gj , F ) p and cpXiF = F (gip ) with a constant c ∈ C∗ . The last equation has p distinct solutions c0 , . . , cp−1 ∈ C∗ , which can be proven to be even eth roots of unity.
After reviewing the bivariate case, a new correspondence is established between planar graphs and minimal resolutions of monomial ideals in three variables. A brief guide is given to the literature on complexity issues and monomial ideals in four or more variables. 1 Introduction A monomial ideal M is an ideal generated by monomials xi11 xi22 · · · xinn in a polynomial ring K[x1 , x2 , . . , xn ]. Monomial ideals are ubiquitous in the study of Gr¨ obner bases. For instance, if I = x4 + y 4 − 1, x7 + y 7 − 2 then its initial ideal with respect to the total degree term order equals M = x4 , x3 y 4 , xy 7 , y 10 .